A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robert VanderPol II
Date: 2017 Nov 18, 20:33 -0800
Thanks Frank, the link gave me half of the root answer I was looking for but did explicitly spell out which was why was the haversine formula developed in the first place and does it still have an advantage:
Historical aside: The height of technology for navigator's calculations used to be log tables. As there is no (real) log of a negative number, the 'versine' enabled them to keep trig functions in positive numbers. Also, the sin2(θ/2) form of the haversine avoided addition (which entailed an anti-log lookup, the addition, and a log lookup). Printed tables for the haversine/inverse-haversine (and its logarithm, to aid multiplications) saved navigators from squaring sines, computing square roots, etc - arduous and error-prone activities.
It seems like it still has an advantage over the cosine formula if you are doing things manually, but other manual methods have things to recommend depending on where your priorities are for speed, accuracy, space considerations and error proneness.
It sound like computationally the cosine formula is now the way to go.